From the right triangle ABC, we have

\(\displaystyle\therefore{\sin{{\left({A}\right)}}}=\frac{{{B}{C}}}{{{A}{C}}}\)

\(\displaystyle\Rightarrow{\sin{{\left({30}^{\circ}\right)}}}=\frac{{v}}{{6}}\)

\(\displaystyle\Rightarrow{1}=\frac{{v}}{{3}}\)

\(\displaystyle\Rightarrow{v}={3}\)

From the right triangle ABC, we have

\(\displaystyle\therefore{\cos{{\left({A}\right)}}}=\frac{{{A}{B}}}{{{A}{C}}}\)

\(\displaystyle\Rightarrow{\cos{{\left({30}^{\circ}\right)}}}=\frac{{u}}{{6}}\)

\(\displaystyle\Rightarrow\frac{\sqrt{{3}}}{{2}}=\frac{{u}}{{6}}\)

\(\displaystyle\Rightarrow\sqrt{{3}}=\frac{{u}}{{3}}\)

\(\displaystyle\Rightarrow{u}={3}\sqrt{{3}}\)

Since, the sum of all angles of a triangle is \(\displaystyle{180}^{\circ}\)

\(\displaystyle\therefore\angle{A}+\angle{B}+\angle{C}={180}^{\circ}\)

\(\displaystyle\Rightarrow{30}^{\circ}+{90}^{\circ}+\angle{C}={180}^{\circ}\)

\(\displaystyle\Rightarrow{120}^{\circ}+\angle{C}={180}^{\circ}\)

\(\displaystyle\Rightarrow\angle{C}={60}^{\circ}\)

\(\displaystyle\therefore{\sin{{\left({A}\right)}}}=\frac{{{B}{C}}}{{{A}{C}}}\)

\(\displaystyle\Rightarrow{\sin{{\left({30}^{\circ}\right)}}}=\frac{{v}}{{6}}\)

\(\displaystyle\Rightarrow{1}=\frac{{v}}{{3}}\)

\(\displaystyle\Rightarrow{v}={3}\)

From the right triangle ABC, we have

\(\displaystyle\therefore{\cos{{\left({A}\right)}}}=\frac{{{A}{B}}}{{{A}{C}}}\)

\(\displaystyle\Rightarrow{\cos{{\left({30}^{\circ}\right)}}}=\frac{{u}}{{6}}\)

\(\displaystyle\Rightarrow\frac{\sqrt{{3}}}{{2}}=\frac{{u}}{{6}}\)

\(\displaystyle\Rightarrow\sqrt{{3}}=\frac{{u}}{{3}}\)

\(\displaystyle\Rightarrow{u}={3}\sqrt{{3}}\)

Since, the sum of all angles of a triangle is \(\displaystyle{180}^{\circ}\)

\(\displaystyle\therefore\angle{A}+\angle{B}+\angle{C}={180}^{\circ}\)

\(\displaystyle\Rightarrow{30}^{\circ}+{90}^{\circ}+\angle{C}={180}^{\circ}\)

\(\displaystyle\Rightarrow{120}^{\circ}+\angle{C}={180}^{\circ}\)

\(\displaystyle\Rightarrow\angle{C}={60}^{\circ}\)